Session: Wednesday Afternoon, May 15

Time: 1:45

The presence of localized modes in repetitive structures (i.e., systems
composed of identical substructural elements) often gives rise to motions during
which vibrational energy becomes spatially confined to a subset of elements.
Such modes have been shown to be generated through eignevalue veering in weakly
mistuned linear systems and mode bifurca-tions in perfectly tuned nonlinear
systems. Recent work by the author has investigated the combined influences of
weak nonlinearities and weak structural mistunings in generating localized
modes. In the present work, the forced response of nonlinear cyclic systems with
structural mistunings is investigated via the method of multiple scales. Under
harmonic excitations, strongly and weakly localized motions will be shown to
exist for various structural parameters. Sample calculations will be presented
for systems composed of two, three, and four degrees of freedom. Additionally,
motion confinement characteristics of such systems will be demonstrated for
transient loading conditions, and the implications for novel vibration isolation
designs will be discussed.